Determination of the maximum scan-gain contours of a beam-scanning paraboloid and their relation to the Petzval surface

The scan-plane fields in the focal region of a beam-scanning paraboloid are determined from physical optics. Amplitude and phase contours are presented, and comparisons are made with the geometrical-optics results. Contours for maximum scan-gain are determined as a function of and illumination taper and compared with the Petzval surface. Unless the is very large or spillover is excessive, a higher scan gain is achieved when the axis of a directional feed is parallel to the axis of the reflector than when the feed is directed toward the vertex. The contour of maximum scan-gain is a function of both illumination taper and . In general, larger values tend to have a maximum-gain contour close to the focal plane, while the smaller values tend to have a maximum-gain contour closer to the Petzval surface. Increasing the illumination taper moves the maximum-gain contour closer to the Petzval surface. Normalized maximum-gain contours are presented as a function of beamwidths of scan. The frequency dependence of these results is discussed.